CN112398397A - Linear active disturbance rejection permanent magnet synchronous motor control method based on model assistance - Google Patents

Linear active disturbance rejection permanent magnet synchronous motor control method based on model assistance Download PDF

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CN112398397A
CN112398397A CN202011367554.7A CN202011367554A CN112398397A CN 112398397 A CN112398397 A CN 112398397A CN 202011367554 A CN202011367554 A CN 202011367554A CN 112398397 A CN112398397 A CN 112398397A
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motor
state
formula
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CN112398397B (en
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邢科新
权欣文
林叶贵
吴昊
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Zhejiang University of Technology ZJUT
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22—Current control, e.g. using a current control loop
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
    • H02P27/085—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation wherein the PWM mode is adapted on the running conditions of the motor, e.g. the switching frequency
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
    • H02P27/12—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque control

Abstract

The invention discloses a model-assisted linear active disturbance rejection permanent magnet synchronous motor control method, which comprises the following steps of 1) firstly building models of a current loop and a speed loop of a permanent magnet synchronous motor; step 2) rewriting a current state equation, and step 3) designing a current loop first-order linear active disturbance rejection controller; step 4) discretization of the constructed controller is needed; step 5), designing a tracking differentiator of the velocity loop first-order model auxiliary linear active disturbance rejection controller; step 6) rewriting a motion state equation: step 7), designing a first-order model compensation linear extended state observer of the speed loop; step 8), selecting upper selection forgetting factor recursive least square method parameter identification; step 9) identifying the rotational inertia and the friction coefficient of the motor when identifying the rotational inertia and the friction coefficient of the motor; and the control precision and the anti-interference capability under the actual working condition are improved.

Description

Linear active disturbance rejection permanent magnet synchronous motor control method based on model assistance
Technical Field
The invention relates to the field of permanent magnet synchronous motor servo control, in particular to a model-assisted linear active disturbance rejection permanent magnet synchronous motor control method.
Background
The permanent magnet synchronous motor has the remarkable advantages of simple structure, reliable operation, small volume, light weight, small loss, high efficiency, flexible and various shapes and sizes of the motor and the like. Since the 21 st century, the material technology is developed vigorously, the performance of permanent magnet materials is improved continuously, the control technology of permanent magnet motors is developed continuously, and the permanent magnet synchronous motors are widely applied to the fields of civil use, aviation, military and the like. However, the permanent magnet synchronous motor is a complex object with multivariable, strong coupling, nonlinearity and variable parameters, and in order to improve the control accuracy of the permanent magnet synchronous motor, some specific control algorithms must be adopted for the permanent magnet synchronous motor.
The most widely used servo control of permanent magnet synchronous motors is vector control. The control of a permanent magnet synchronous motor is generally divided into three-loop control: current loop, speed loop, position loop. Common control algorithms are: traditional PID control, synovial membrane control, adaptive control, model predictive control, active disturbance rejection control, etc. Because the algorithm is simple and high in applicability, the requirement on the parameters of the controlled object is less, and the traditional PID technology is still the algorithm with the largest use amount in the field of industrial control drivers nowadays. The active disturbance rejection control is the inheritance and development of the traditional PID control, and is slowly applied to the design of a motor driver by engineers in recent years due to strong applicability and strong disturbance rejection.
ADRC is proposed by the researchers in Konjin Qing of Chinese academy of sciences, and the idea is to extract disturbance information from the system according to the output and input of the system, wherein the disturbance information is composed of internal disturbance and external disturbance, so that the disturbance can be also called total disturbance. And the total disturbance is eliminated by using the control signal, so that the influence of the disturbance quantity on the controlled quantity is improved. In the 90 s of the 20 th century, the active disturbance rejection technology was introduced into the united states, and in order to enable the active disturbance rejection technology to be really applied to industrialization, the high-minded doctor converts the nonlinear active disturbance rejection technology into the linear active disturbance rejection technology, and combines the parameters of the active disturbance rejection controller with the bandwidth, so that the parameter adjusting process is simplified. Meanwhile, when the active-disturbance-rejection control is designed, the known model information of the controlled object can be fused into the controller, so that the disturbance rejection of the controller is increased.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a model-assisted linear active disturbance rejection permanent magnet synchronous motor control method.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a linear active disturbance rejection permanent magnet synchronous motor control method based on model assistance is characterized by comprising the following steps:
step 1) firstly, building models of a current loop and a speed loop of a permanent magnet synchronous motor;
the stator voltage equation of the motor is as follows:
Figure BDA0002805009400000021
in the formula: u. ofdDenotes the d-axis voltage, uqRepresenting the q-axis voltage, weIndicating the motor speed, idRepresenting the real-time current of the d-axis, iqRepresenting the real-time current of the q-axis, R being the stator resistance,. psiqIs a component of the stator flux linkage q-axis, psidIs the component of the stator flux linkage on the d-axis;
the stator flux linkage equation is:
Figure BDA0002805009400000031
in the formula LdRepresenting the inductance on the d-axis of the stator winding, LqRepresenting the inductance in the q-axis of the stator winding,. psifPermanent magnet fundamental flux linkage;
substituting equation (2) for equation (1) yields the stator voltage equation:
Figure BDA0002805009400000032
because the controlled object is a surface-mounted permanent magnet synchronous motor, Ld＝LqThe current state equation under the coordinate axes d and q can be obtained as follows:
Figure BDA0002805009400000033
wherein L is the inductance of the stator,
Figure BDA0002805009400000034
permanent magnet fundamental flux linkage;
d. the kinematic state equation under the q coordinate axis is:
Figure BDA0002805009400000035
wherein B is the coefficient of viscous friction, J is the moment of inertia, npIs the number of pole pairs, TLIs the load torque;
step 2) rewriting the current state equation into:
Figure BDA0002805009400000036
in the formula (6) fd is knownAnd fq is knownFor known object information, it can be obtained by least squares parameter identification after the velocity reaches steady state, fd' and fq' as unknown disturbance, fd＝fd is known+fd' and fq＝fq is known+fqIs unknown disturbanceAnd the integration of the known object information, which is regarded as the expansion of the disturbance; in the formula (6) fdAnd fqExpressed as:
Figure BDA0002805009400000041
step 3), designing a current loop first-order linear active disturbance rejection controller; because the input of the current loop is continuously changed and does not generate step-like signals like a speed loop, in order to avoid the phase lag of the current loop, a tracking differentiator is not needed in the design of the current loop, and a first-order linear active disturbance rejection controller is expressed as follows:
Figure BDA0002805009400000042
the state matrix a and the input matrix without model assistance are:
Figure BDA0002805009400000043
b0it is shown that for one of the variables,
Figure BDA0002805009400000044
Figure BDA0002805009400000045
for the derivative of the actual unknown total disturbance, a model-assisted active disturbance rejection controller is adopted, and the state matrix A and the input matrix B need to comprise more object information; the known information of the model can be fused into a state matrix and an input matrix according to the formula (7); for a d-axis current loop, let x ═ id fd]T，u＝udObtain the state matrix thereof
Figure BDA0002805009400000046
Input matrix
Figure BDA0002805009400000047
Similarly, for a q-axis current loop, let x ═ iq fq]T,u＝uqRest moments of stateArray AqAnd AdSame, input matrix BqAnd BdThe same; the linear extended observer of the model-assisted active disturbance rejection controller is expressed as:
Figure BDA0002805009400000048
the A and B matrix values in the formula are calculated as above, ucFor combined input, ycIs an output; z is the state vector of the observer, and the output matrix C is [ 10 ]]TAnd L is an observer gain matrix required to be designed, and meanwhile, for simplicity in design, the poles of the observer characteristic equation are placed at the same position, so that the observer gain matrix can be obtained:
λ(s)＝|sI-(A-LC)|＝(s+w0)2#(10)
wherein w0Is the pole position, I is the identity matrix; s is its pole position.
The gain matrix L of the linear state observer is thus:
L＝[l1 l2]T#(11)
can be calculated to obtain l1，l2The values of (A) are:
Figure BDA0002805009400000051
step 4) in order to enable the control algorithm to be used in practical application, discretization is needed for the constructed controller, and the linear model auxiliary extended state observer corresponding to the discretization can be obtained as follows:
Figure BDA0002805009400000052
in the formula ud(k) As a combination of inputs to the observer, yd(k) For the output combination of the observer, phi, gamma and H are respectively corresponding to the state matrix, input matrix and output matrix of the continuous system one by one, LcIs the gain matrix of the observer in a discrete state, z (k) isThe state vector of the post observer is scattered.
Step 5) designing a tracking differentiator of the velocity loop first-order model auxiliary linear active disturbance rejection controller, wherein the velocity is given to be a step signal generally, so that the transition process arrangement needs to be carried out on the given velocity step signal, and the model of the tracking differentiator is as follows:
Figure BDA0002805009400000053
the nonlinear function fal in equation (14) is defined as:
Figure BDA0002805009400000061
sign in the formula (15) represents a sign function, δ0Denotes the filter scale, α0Is taken to be between 0 and 1, e0State variables representing the system;
step 6) rewriting the motion state equation into:
Figure BDA0002805009400000062
in the formula (16), the compound represented by the formula,
Figure BDA0002805009400000063
in order to know the controlled object information of the speed ring,
Figure BDA0002805009400000064
for the unknown disturbance of the velocity loop,
Figure BDA0002805009400000065
the sum of the unknown disturbance and the known information of the speed ring can be regarded as the expansion of the disturbance; the known speed ring controlled object information in equation (16) is:
Figure BDA0002805009400000066
step 7), designing a first-order model compensation linear extended state observer of the speed loop; the same as the current loop, a first-order controller is adopted, the basic form of the model is shown as the formula (8), and for the speed loop, the state matrix of the speed loop
Figure BDA0002805009400000067
Input matrix
Figure BDA0002805009400000068
The extended state observer is given by the formula (9), and its output matrix C is [ 10 ═ C]Of its gain matrix l1，l2The values of (A) are as follows:
Figure BDA0002805009400000069
the discretization of the speed loop is the same as that of the current loop;
step 8) because the inductance and the resistance value of the motor change along with the temperature and the humidity, and belong to the condition that the parameters change slowly, the forgetting factor recursive least square method parameter identification is selected in the selection of the parameter identification method, meanwhile, the rotational inertia is identified by adopting a forgetting factor recursive least square algorithm, and the formula of the forgetting factor recursive least square parameter estimation is as follows:
Figure BDA0002805009400000071
in the formula (19), λ represents a forgetting factor and needs to be selected to be a positive number close to 1,
Figure BDA0002805009400000072
the data vector at time k is selected to be P (0) ═ α I for the initial value P (0), α is a sufficiently large positive real number, I is an identity matrix, and for the initial value P (0), the data vector at time k is selected to be
Figure BDA0002805009400000073
Take a value of
Figure BDA0002805009400000074
ε is the zero vector. In the formula (19)
Figure BDA0002805009400000075
As an estimate, it is expressed as:
Figure BDA0002805009400000076
step 9) before the motor is started with load, firstly identifying the rotational inertia and the friction coefficient of the motor, and when identifying the rotational inertia and the friction coefficient of the motor, requiring the motor to operate under the condition of no load for identification; loaded torque T due to no load conditionLWhen the motor is equal to 0, the motion equation of the motor is obtained as follows:
Figure BDA0002805009400000077
wherein the electromagnetic torque TeExpressed as:
Figure BDA0002805009400000078
the motor firstly works at a constant speed stage, and the obtained speed differential term is zero, so that the following conditions can be obtained:
Te＝Bwe
the friction coefficient can be identified firstly, the friction coefficient is substituted into a motion equation, an acceleration and deceleration process is arranged for the motor, so that the differential of the speed is not zero, and in the acceleration and deceleration process, forgetting factor recursion least square identification is carried out on sampled data.
The invention has the beneficial effects that: the first-order linear active disturbance rejection controller is used for replacing a traditional PI controller to control the speed and the current of the motor in the current loop and the speed loop, when the speed reaches a stable state, parameters such as motor stator inductance and stator resistance are identified through least square parameter identification, and the identification parameters are added into the first-order model auxiliary linear active disturbance rejection controller, so that the control precision and the disturbance rejection capability under the actual working condition are improved.
Drawings
FIG. 1 is a PMSM motor control block diagram;
FIG. 2 is a schematic diagram of a velocity loop first order model assisted linear active disturbance rejection controller;
fig. 3 is a flow chart of identifying resistance, inductance, flux linkage and moment of inertia by a forgetting factor recursive least square method.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Referring to fig. 1-3, a model-assisted linear active disturbance rejection permanent magnet synchronous motor control method includes the following steps:
step 1) a set speed is given through the MCU, the set speed is required to be below the highest rotating speed, and the accuracy of the set speed is set according to the accuracy of the speed sensor and the sampling period of the sensor. While setting the control period of the speed loop.
And 2) arranging a transition process for the set speed, and adopting a tracking differentiator. Adjusting parameter variables in the fal function, where e0Is an error, α0Has a value range of 0<α0<1,δ0Is a filtering scale. The particular transition may be arranged according to the actual load and the range of the regulation speed.
And 3) taking the difference between the set speed value and the real-time speed value acquired by the encoder as input, inputting the difference into a first-order linear model auxiliary active disturbance rejection controller, and fusing the identified data into the linear model auxiliary active disturbance rejection controller because the rotational inertia and the friction coefficient are identified before the motor runs with load. And setting the bandwidths of the controller and the observer according to the control period, associating adjustable parameters in the controller with the controller bandwidth, and simultaneously determining the relationship between the observer period and the controller period multiple. The value of b is set. Adjusting the relationship between several parameters allows the controller to achieve better results.
And 4) taking the difference between the output of the speed loop controller and the q-axis current value acquired in real time as the input of a q-axis current loop, wherein the current loop does not need a tracking differentiator, so that a first-order linear model of the current loop can be used for assisting the active disturbance rejection controller to carry out parameter adjustment. As with the speed loop, the model assistance function is not enabled during start-up. And setting the control period of the current loop to ensure that the sampling period of the current loop is more than 3 times of that of the speed loop.
And 5) determining the sampling period of the forgetting factor recursive least square identification method, and determining the data variable to be acquired. The data variables to be collected for identifying the inductance here are: real time current i of q axisqRotational speed w of the motoreD-axis voltage ud. The data variables that need to be collected for identifying the resistance parameters are: motor speed weQ-axis voltage uqQ-axis real-time current iq. When the parameter identification algorithm starts to operate, the initial value of the identified parameter is set, and the parameter is required to be a sufficiently small real number. An initial covariance matrix is set, requiring that the value be a sufficiently large real number. The value of the forgetting factor λ is set, which requires the selection of a positive number close to 1, usually not less than 0.9, and is generally selected to range between 0.95 and 1.
And 6) identifying the rotational inertia and the friction coefficient of the motor before the motor normally runs with load, firstly identifying the friction coefficient of the motor when the motor works at a constant speed, substituting the identified friction coefficient into a motion equation, arranging an acceleration and deceleration process for the motor in order to identify the rotational inertia of the motor, acquiring current, flux linkage and rotation speed parameters in the acceleration and deceleration process, and identifying the rotational inertia parameters by using a least square algorithm of a forgetting factor.
And 7) after the rotating speed of the motor reaches the stable rotating speed, the identification data of the resistor, the inductor and the magnetic linkage are fused into the model for model assistance, so that the stability, the rapidity and the anti-interference performance of the controller are improved.
The above examples merely represent one embodiment of the present invention and are not to be construed as limiting the scope of the invention. It should be noted that a person skilled in the art could make several alternative designs without departing from the inventive concept, which falls within the scope of the invention.

Claims (1)

1. A linear active disturbance rejection permanent magnet synchronous motor control method based on model assistance is characterized by comprising the following steps:
step 1) firstly, building models of a current loop and a speed loop of a permanent magnet synchronous motor;
the stator voltage equation of the motor is as follows:
Figure FDA0002805009390000011
in the formula: u. ofdDenotes the d-axis voltage, uqRepresenting the q-axis voltage, weIndicating the motor speed, idRepresenting the real-time current of the d-axis, iqRepresenting the real-time current of the q-axis, R being the stator resistance,. psiqIs a component of the stator flux linkage q-axis, psidIs the component of the stator flux linkage on the d-axis;
the stator flux linkage equation is:
Figure FDA0002805009390000012
in the formula LdRepresenting the inductance on the d-axis of the stator winding, LqRepresenting the inductance in the q-axis of the stator winding,. psifPermanent magnet fundamental flux linkage;
substituting equation (2) for equation (1) yields the stator voltage equation:
Figure FDA0002805009390000013
because the controlled object is a surface-mounted permanent magnet synchronous motor, Ld＝LqThe current state equation under the coordinate axes d and q can be obtained as follows:
Figure FDA0002805009390000021
wherein L is the inductance of the stator,
Figure FDA0002805009390000022
permanent magnet fundamental flux linkage;
d. the kinematic state equation under the q coordinate axis is:
Figure FDA0002805009390000023
wherein B is the coefficient of viscous friction, J is the moment of inertia, npIs the number of pole pairs, TLIs the load torque;
step 2) rewriting the current state equation into:
Figure FDA0002805009390000024
in the formula (6) fd is knownAnd fq is knownFor known object information, it can be obtained by least squares parameter identification after the velocity reaches steady state, fd’And fq’For unknown disturbances, fd＝fd is known+fd’And fq＝fq is known+fq’The method is the integration of unknown disturbance and known object information and is regarded as the expansion of the disturbance; in the formula (6) fdAnd fqExpressed as:
Figure FDA0002805009390000025
step 3), designing a current loop first-order linear active disturbance rejection controller; because the input of the current loop is continuously changed and does not generate step-like signals like a speed loop, in order to avoid the phase lag of the current loop, a tracking differentiator is not needed in the design of the current loop, and a first-order linear active disturbance rejection controller is expressed as follows:
Figure FDA0002805009390000031
the state matrix a and the input matrix without model assistance are:
Figure FDA0002805009390000032
b0it is shown that for one of the variables,
Figure FDA0002805009390000033
Figure FDA0002805009390000034
for the derivative of the actual unknown total disturbance, a model-assisted active disturbance rejection controller is adopted, and the state matrix A and the input matrix B need to comprise more object information; the known information of the model can be fused into a state matrix and an input matrix according to the formula (7); for a d-axis current loop, let x ═ id fd]T，u＝udObtain the state matrix thereof
Figure FDA0002805009390000035
Input matrix
Figure FDA0002805009390000036
Similarly, for a q-axis current loop, let x ═ iq fq]T，u＝uqThe remaining state matrix AqAnd AdSame, input matrix BqAnd BdThe same; the linear extended observer of the model-assisted active disturbance rejection controller is expressed as:
Figure FDA0002805009390000037
the A and B matrix values in the formula are calculated as above, ucFor combined input, ycIs an output; z is the state vector of the observer, and the output matrix C is [ 10 ]]TAnd L is an observer gain matrix required to be designed, and meanwhile, for simplicity in design, the poles of the observer characteristic equation are placed at the same position, so that the observer gain matrix can be obtained:
λ(s)＝|sI-(A-LC)|＝(s+w0)2#(10)
wherein w0Is the pole position, I is the identity matrix; s is its pole position.
The gain matrix L of the linear state observer is thus:
L＝[l1 l2]T#(11)
can be calculated to obtain l1，l2The values of (A) are:
Figure FDA0002805009390000041
step 4) in order to enable the control algorithm to be used in practical application, discretization is needed for the constructed controller, and the linear model auxiliary extended state observer corresponding to the discretization can be obtained as follows:
Figure FDA0002805009390000042
in the formula ud(k) As a combination of inputs to the observer, yd(k) For the output combination of the observer, phi, gamma and H are respectively corresponding to the state matrix, input matrix and output matrix of the continuous system one by one, LcIs the observer gain matrix in the discrete state, and z (k) is the discrete post observer state vector.
Step 5) designing a tracking differentiator of the velocity loop first-order model auxiliary linear active disturbance rejection controller, wherein the velocity is given to be a step signal generally, so that the transition process arrangement needs to be carried out on the given velocity step signal, and the model of the tracking differentiator is as follows:
Figure FDA0002805009390000043
the nonlinear function fal in equation (14) is defined as:
Figure FDA0002805009390000044
sign in the formula (15) represents a sign function, δ0Denotes the filter scale, α0Is taken to be between 0 and 1, e0State variables representing the system;
step 6) rewriting the motion state equation into:
Figure FDA0002805009390000045
in the formula (16), the compound represented by the formula,
Figure FDA0002805009390000046
in order to know the controlled object information of the speed ring,
Figure FDA0002805009390000047
for the unknown disturbance of the velocity loop,
Figure FDA0002805009390000051
the sum of the unknown disturbance and the known information of the speed ring can be regarded as the expansion of the disturbance; the known speed ring controlled object information in equation (16) is:
Figure FDA0002805009390000052
step 7), designing a first-order model compensation linear extended state observer of the speed loop; the same as the current loop, a first-order controller is adopted, the basic form of the model is shown as the formula (8), and for the speed loop, the state matrix of the speed loop
Figure FDA0002805009390000053
Input matrix
Figure FDA0002805009390000054
The extended state observer is given by the formula (9), and its output matrix C is [ 10 ═ C]Moment of gain thereofArray l1，l2The values of (A) are as follows:
Figure FDA0002805009390000055
the discretization of the speed loop is the same as that of the current loop;
step 8) because the inductance and the resistance value of the motor change along with the temperature and the humidity, and belong to the condition that the parameters change slowly, the forgetting factor recursive least square method parameter identification is selected in the selection of the parameter identification method, meanwhile, the rotational inertia is identified by adopting a forgetting factor recursive least square algorithm, and the formula of the forgetting factor recursive least square parameter estimation is as follows:
Figure FDA0002805009390000056
in the formula (19), λ represents a forgetting factor and needs to be selected to be a positive number close to 1,
Figure FDA0002805009390000057
the data vector at time k is selected to be P (0) ═ α I for the initial value P (0), α is a sufficiently large positive real number, I is an identity matrix, and for the initial value P (0), the data vector at time k is selected to be
Figure FDA0002805009390000061
Take a value of
Figure FDA0002805009390000062
ε is the zero vector. In the formula (19)
Figure FDA0002805009390000063
As an estimate, it is expressed as:
Figure FDA0002805009390000064
step 9) before the motor is started with load,firstly, identifying the rotational inertia and the friction coefficient of the motor, and when identifying the rotational inertia and the friction coefficient of the motor, requiring the motor to operate under the condition of no load for identification; loaded torque T due to no load conditionLWhen the motor is equal to 0, the motion equation of the motor is obtained as follows:
Figure FDA0002805009390000065
wherein the electromagnetic torque TeExpressed as:
Figure FDA0002805009390000066
the motor firstly works at a constant speed stage, and the obtained speed differential term is zero, so that the following conditions can be obtained:
Te＝Bwe
the friction coefficient can be identified firstly, the friction coefficient is substituted into a motion equation, an acceleration and deceleration process is arranged for the motor, so that the differential of the speed is not zero, and in the acceleration and deceleration process, forgetting factor recursion least square identification is carried out on sampled data.
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